Algebra Examples

$(2 \sqrt{- 54}) (10 \sqrt{48})$

Step 1

Rewrite $- 54$ as $- 1 (54)$ .

$2 \sqrt{- 1 (54)} (10 \sqrt{48})$

Step 2

Rewrite $\sqrt{- 1 (54)}$ as $\sqrt{- 1} \cdot \sqrt{54}$ .

$2 (\sqrt{- 1} \cdot \sqrt{54}) (10 \sqrt{48})$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$2 (i \cdot \sqrt{54}) (10 \sqrt{48})$

Step 4

Rewrite $54$ as $3^{2} \cdot 6$ .

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Step 4.1

Factor $9$ out of $54$ .

$2 (i \cdot \sqrt{9 (6)}) (10 \sqrt{48})$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$2 (i \cdot \sqrt{3^{2} \cdot 6}) (10 \sqrt{48})$

$2 (i \cdot \sqrt{3^{2} \cdot 6}) (10 \sqrt{48})$

Step 5

Pull terms out from under the radical.

$2 (i \cdot (3 \sqrt{6})) (10 \sqrt{48})$

Step 6

Simplify the expression.

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Step 6.1

Move $3$ to the left of $i$ .

$2 (3 \cdot i \sqrt{6}) (10 \sqrt{48})$

Step 6.2

Multiply $3$ by $2$ .

$6 (i \sqrt{6}) (10 \sqrt{48})$

$6 (i \sqrt{6}) (10 \sqrt{48})$

Step 7

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 7.1

Factor $16$ out of $48$ .

$6 i \sqrt{6} (10 \sqrt{16 (3)})$

Step 7.2

Rewrite $16$ as $4^{2}$ .

$6 i \sqrt{6} (10 \sqrt{4^{2} \cdot 3})$

$6 i \sqrt{6} (10 \sqrt{4^{2} \cdot 3})$

Step 8

Pull terms out from under the radical.

$6 i \sqrt{6} (10 (4 \sqrt{3}))$

Step 9

Multiply $4$ by $10$ .

$6 i \sqrt{6} (40 \sqrt{3})$

Step 10

Multiply $6 i \sqrt{6} (40 \sqrt{3})$ .

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Step 10.1

Multiply $40$ by $6$ .

$240 i \sqrt{6} \sqrt{3}$

Step 10.2

Combine using the product rule for radicals.

$240 i \sqrt{3 \cdot 6}$

Step 10.3

Multiply $3$ by $6$ .

$240 i \sqrt{18}$

$240 i \sqrt{18}$

Step 11

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 11.1

Factor $9$ out of $18$ .

$240 i \sqrt{9 (2)}$

Step 11.2

Rewrite $9$ as $3^{2}$ .

$240 i \sqrt{3^{2} \cdot 2}$

$240 i \sqrt{3^{2} \cdot 2}$

Step 12

Pull terms out from under the radical.

$240 i (3 \sqrt{2})$

Step 13

Multiply $3$ by $240$ .

$720 i \sqrt{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$